math destroyer test 2 number 13

[wall1two]

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james can paint a room in 4 hours, mike can do a room in 5. how long does it take both of them to paint a room if james works only 1 hour.

i understand how they reached their answer:

james in one hour does 1/4 of the room.

so 3/4 of the room @ 1/5 of the room an hour:

3/4= x * 1/5 x= 3 3/4 hours

but i disagree . that first hour 1/4 of the room does not get done. 9/20 of the room gets done. if james does 1/4 and mike does a 1/5 then together 9/20 got done meaning it should take an additional x hours. what am i missing>?

11/20 = x * 1/5

 

[AmpedUp]

Here's my most intuitive approach (the only way I know how to approach this problem):

1/4 + 1/5 = 9/20 of work is finished in the first hour.

1 - 9/20 = 11/20 or 55% of the work in the room still remains.

Mike can do a whole room in 5 hours. Take 55% of 5 hours, which is 2.75 or 2 hrs and 45 minutes.

Now, add up the times: 1 hr (James & Mike working together) + 2 hrs 45 min (Mike working alone) = 3 hrs and 45 min.

 

[wall1two]

Here's my most intuitive approach (the only way I know how to approach this problem):

1/4 + 1/5 = 9/20 of work is finished in the first hour.

1 - 9/20 = 11/20 or 55% of the work in the room still remains.

Mike can do a whole room in 5 hours. Take 55% of 5 hours, which is 2.75 or 2 hrs and 45 minutes.

Now, add up the times: 1 hr (James & Mike working together) + 2 hrs 45 min (Mike working alone) = 3 hrs and 45 min.

i forgot to add in that first hour!! thanks alot

 

[dentalWorks]

You can also solve this using simple rate equation:

(Rate)(time) = work done (in this case, work = 1 room)

Rate of James = 1 room / 4 hours
Rate of Mike = 1 room / 5 hours

so...

Work done by James + Work done by Mike = 1 room

(1/4)(1 hr) + (1/5)(x hrs) = 1 room

Solve for x and x = 3 3/4